Finite Group Databasebeta

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C4×H(5,𝔽2)×D73 #33992583

order18688
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×H(5,𝔽2)×D73

Splittings

FittingC4×H(5,𝔽2)×C73 ⋊ C2
SylowC73 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C24×D73
commutatorC2×C73C25×C4
FrattiniC22C25×D73
FittingC4×H(5,𝔽2)×C73C2
socle, cosocleC22×C73C26
prime radicalC2×H(5,𝔽2)×D73C2
hypercenterC4×H(5,𝔽2)D73
hypocenterC73C2×C4×H(5,𝔽2)
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

12378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

2584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1076167);