C₇×D₁₁×D₉₉ #44478959

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₁₁×D₉₉
unambiguous semidirect product	(C₉×D₁₁)⋊(C₇×D₁₁)
unambiguous semidirect product	(C₁₁×D₁₁)⋊(C₇×D₉)

Splittings

Fitting, Hall	C₇×C₉×C₁₁² ⋊ C₂²
derived, Hall	C₉×C₁₁² ⋊ C₂²×C₇
Hall	C₇×C₁₁² ⋊ C₂×D₉
Sylow	C₁₁² ⋊ C₂×C₇×D₉
Hall	C₇×C₉ ⋊ D₁₁²
Sylow	C₉ ⋊ C₇×D₁₁²

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₁₁×D₉₉
commutator, cosocle, hypocenter	C₉×C₁₁²	C₂²×C₇
Frattini	C₃	C₇×D₁₁×D₃₃
Fitting	C₇×C₉×C₁₁²	C₂²
socle	C₃×C₇×C₁₁²	C₂×D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₇

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1386

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3,4,5,6,7)(9,11)(10,14)(12,13)(15,16)(17,18,20,22,24,26,27,25,23,21,19)(29,30)(31,32)(33,34)(35,36)(37,38);(8,13,15,14,9,11,10,16,12)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29,31,33,35,37,38,36,34,32,30)

Conjugacy classes & character table

2499 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 182);