Finite Group Databasebeta

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C₂×C₄×#14556670 #34030512

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

C₂×C₄×#14556670

Splittings

Fitting	C₂²×C₄²×C₇₃ ⋊ C₄
Sylow	C₇₃ ⋊ C₂×C₄×#117

Subgroups

	subgroup	G/H
center	C₂×C₄²	C₂×#64408
commutator	C₂×C₇₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#64408
Fitting	C₂²×C₄²×C₇₃	C₄
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂⁴×D₇₃	C₂³
cosocle	C₂²×D₇₃	C₂⁵
hypercenter	C₂²×C₄²	#64408
hypocenter	C₇₃	C₂×C₄×#117
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄²

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4672

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1114096);