Finite Group Databasebeta

← Prev (#63765) Next (#63767) →

C₈×#157 #63766

order	288
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₃×C₄

Aliases

Splittings

Fitting	C₃²×C₈ ⋊ C₄
derived, Sylow	C₃² ⋊ C₄×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₈	#157
commutator, hypocenter	C₃²	C₄×C₈
Frattini	C₄	C₂×#157
Fitting	C₃²×C₈	C₄
socle	C₂×C₃²	C₄²
prime radical	C₂×C₃⋊D₃	C₂×C₄
cosocle	C₄×C₃⋊D₃	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₈

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 14 points:

(1,2)(3,5,6,4);(1,3,6)(2,5,4)(7,8,9,11,10,12,13,14)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#72252853
maximal subgroup of	#10590022, #10590023, #10590082, …
maximal normal subgroup of	#10590022, #10590023, #10590082, …
maximal quotient of	C₁₆×#157, #10590135, C₈×#622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 414);