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C2×#20243705 #26217478

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20243705

Splittings

FittingC23×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#1874

Subgroups

subgroupG/H
centerC24C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC23×C4⋊C4×C47C2
socleC24×C47C2×D4
prime radicalC22×#13093998C2
cosocleC22×C4×C47C24
hypercenterC23×C4⋊C4D47
hypocenterC47C2×#1874
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

2614 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170768);