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C4×#15689291 #26222152

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#15689291

Splittings

FittingC4×H(5,𝔽2)×C47 ⋊ C2
SylowC47 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2×C4#13093993
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×H(5,𝔽2)×C47C2
socleC22×C47C2×#120
prime radicalC2×#15689291C2
cosocleC22×C4×C47C24
hypercenterC4×H(5,𝔽2)D47
hypocenterC47C4×#453
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×H(5,𝔽2)

1578 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 175442);