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C₂×D₄₈ #4902

order	192
isoclinism	isoclinic class of D₄₈
automorphism	Aut(G) order 6144
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₄₈

Splittings

Fitting	C₂×C₃×C₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₁₆

Subgroups

	subgroup	G/H
center	C₂²	D₂₄
commutator, cosocle	C₃×C₈	C₂³
Frattini	C₈	C₂²×D₃
Fitting	C₂×C₃×C₁₆	C₂
socle	C₂²×C₃	D₈
hypercenter	C₂×C₁₆	D₃
hypocenter	C₃	C₂×D₁₆
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 21 points:

(3,4,5)(6,7,12,18,9,13,16,19,10,14,20,21,15,17,8,11);(1,2)(4,5)(7,11)(8,12)(9,15)(13,21)(14,19)(16,20)(17,18);(1,2)

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#67577, #67583, #67596, …
maximal normal subgroup of	#67577, #67583, #67596, …
maximal quotient of	#69044, C₄×D₄₈, #69058, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 461);