C₄×Dic₂₃ #67268

order	368
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product	C₄×Dic₂₃
unambiguous semidirect product	C₂₃⋊C₄²

Splittings

derived, Sylow

C₂₃ ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	D₂₃
commutator, hypocenter	C₂₃	C₄²
Frattini	C₂²	C₂×D₂₃
Fitting	C₂×C₄×C₂₃	C₂
socle, prime radical, cosocle	C₂²×C₂₃	C₂²
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₄

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₈×Dic₂₃, Dic₂₃⋊C₈, #10624997, …
maximal normal subgroup of	C₈×Dic₂₃, Dic₂₃⋊C₈, #10624997, …
maximal quotient of	C₄×C₂₃⋊C₈, #10624985, C₈×Dic₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(368, 10);

C4×Dic23 #67268

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₄×Dic₂₃ #67268