Finite Group Databasebeta

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C2×C4⋊#10597845 #19097849

order5024
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊#10597845
unambiguous semidirect productD157⋊(C4⋊C4)

Splittings

FittingC2×C4×C157 ⋊ C4
SylowC157 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC22C2×#10597845
commutatorC2×C157C22×C4
FrattiniC2C22×#10597845
FittingC2×C4×C157C4
socleC22×C157C2×C4
hypercenterC2×C4#10597845
hypocenterC157C2×C4⋊C4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

332 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5024, 224);