C₇×C₁₁⋊(C₁₃⋊D₁₃) #39907364

order	26026
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₇×C₁₁⋊(C₁₃⋊D₁₃)
unambiguous semidirect product	C₁₁⋊(C₇×C₁₃⋊D₁₃)
unambiguous semidirect product	C₁₃⋊(C₇×D₁₄₃)

Splittings

Fitting, socle, Hall	C₇×C₁₁×C₁₃² ⋊ C₂
derived, Hall	C₁₁×C₁₃² ⋊ C₂×C₇
Hall	C₇×C₁₃² ⋊ D₁₁
Sylow	C₁₃² ⋊ C₇×D₁₁
Hall	C₇×C₁₁ ⋊ C₁₃⋊D₁₃
Sylow	C₁₁ ⋊ C₇×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₇	C₁₁⋊(C₁₃⋊D₁₃)
commutator, cosocle, hypocenter	C₁₁×C₁₃²	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃²	C₂
LCS	G ▷ C₁₁×C₁₃²
UCS	C₁ ◁ C₇

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 13013

A minimal faithful permutation representation — 3 generators on 44 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44);(8,9,11,13,15,17,18,16,14,12,10)(32,33,35,37,39,41,43,44,42,40,38,36,34);(19,20,22,24,26,28,30,31,29,27,25,23,21)

Conjugacy classes & character table

6517 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26026, 20);

C7×C11⋊(C13⋊D13) #39907364