Finite Group Databasebeta

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C2×C4×Dic376 #26369554

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic376

Splittings

SylowC47 ⋊ C2×C4×Q32

Subgroups

subgroupG/H
centerC22×C4D376
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C4×C16×C47C2
socle, prime radicalC23×C47C2×D8
cosocleC2×C8×C47C24
hypercenterC2×C4×C16D47
hypocenterC47C2×C4×Q32
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

678 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322844);