Finite Group Databasebeta

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C4×#15688850 #26106873

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#15688850

Splittings

FittingC4×C4⋊C8×C47 ⋊ C2
SylowC47 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D47
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC4×C4⋊C8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenterC4×C4⋊C8D47
hypocenterC47C4×D4⋊C8
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60163);