Finite Group Databasebeta

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C2×Q8×C4⋊Dic47 #26375581

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×C4⋊Dic47

Splittings

SylowC47 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×C4×Q8×C47C2
socle, prime radicalC24×C47C24
cosocleC23×C47C25
hypercenterC22×C4×Q8D47
hypocenterC47C2×Q8×C4⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×Q8

3246 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328871);