Finite Group Databasebeta

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C8×#13093989 #26214883

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#13093989

Splittings

SylowC47 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC8×C4⋊C4×C47C2
socle, prime radicalC23×C47C23×C4
cosocleC22×C4×C47C24
hypercenterC8×C4⋊C4D47
hypocenterC47C4×C8×Q8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1070 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168173);