Finite Group Databasebeta

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C2×#14558482 #18011048

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14558482
unambiguous semidirect productD37⋊#387

Splittings

FittingC2×C4⋊C4×C37 ⋊ C4
SylowC37 ⋊ C2×#387

Subgroups

subgroupG/H
centerC23C22×#3866
commutatorC22×C37C23×C4
FrattiniC22C23×#3866
FittingC2×C4⋊C4×C37C4
socleC23×C37C22×C4
prime radicalC23×D37C23
cosocleC22×D37C24
hypercenterC2×C4⋊C4#3866
hypocenterC37C2×#387
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C4⋊C4

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1184

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 20962);