C₇×C₂²⋊D₂₅ #13063734

order	1400
isoclinism	isoclinic class of Dic₅₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₂²⋊D₂₅
unambiguous semidirect product	C₂²⋊(C₇×D₂₅)

Splittings

Fitting	C₂²×C₇×C₂₅ ⋊ C₂
Hall	C₇×C₂₅ ⋊ D₄
Sylow	C₂₅ ⋊ C₇×D₄

Subgroups

	subgroup	G/H
center	C₂×C₇	C₂×D₂₅
commutator, cosocle	C₂×C₂₅	C₂²×C₇
Frattini	C₂×C₅	C₂×C₇×D₅
Fitting	C₂²×C₇×C₂₅	C₂
socle	C₂×C₅×C₇	C₂×D₅
hypercenter	C₂²×C₇	D₂₅
hypocenter	C₂₅	C₇×D₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₇ ◁ C₂²×C₇

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 700

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 23);

C7×C22⋊D25 #13063734