Finite Group Databasebeta

C2×#27131659 #37566986

order24352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27131659

Splittings

SylowC761 ⋊ C2×M16

Subgroups

subgroupG/H
centerC22C2×#15690200
commutatorC2×C761C22×C4
FrattiniC2C22×#15690200
FittingC2×C4×C761C4
socleC22×C761C2×C4
prime radicalC22×D761C4
cosocleDic761C23
hypercenterC2×C4#15690200
hypocenterC761C2×M16
LCSG ▷ C2×C761 ▷ C761
UCSC1 ◁ C22 ◁ C2×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12176

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24352, 232);