Finite Group Databasebeta

C2×D6184 #37613001

order24736
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D6184

Splittings

FittingC2×C8×C773 ⋊ C2
SylowC773 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22D3092
commutator, cosocleC4×C773C23
FrattiniC4C22×D773
FittingC2×C8×C773C2
socleC22×C773D4
hypercenterC2×C8D773
hypocenterC773C2×D8
LCSG ▷ C4×C773 ▷ C2×C773 ▷ C773
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12368

Conjugacy classes & character table

6190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24736, 157);