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C₂³×D₂₈ #90605

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂³×D₂₈

Splittings

Fitting	C₂³×C₄×C₇ ⋊ C₂
Sylow	C₇ ⋊ C₂³×D₄

Subgroups

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator, cosocle	C₂×C₇	C₂⁵
Frattini	C₂	C₂⁴×D₇
Fitting	C₂³×C₄×C₇	C₂
socle	C₂⁴×C₇	C₂²
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂³×D₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 5 generators on 17 points:

(7,8,9,10)(11,12,14,16,17,15,13);(1,2)(3,4)(5,6)(8,10)(12,13)(14,15)(16,17);(5,6);(3,4);(1,2)

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11727180, #11727275, #11727713, …
maximal normal subgroup of	#11727180, #11727275, #11727713, …
maximal quotient of	C₂²×#6432, C₂²×C₄×D₂₈, C₂²×#6438, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1367);