Finite Group Databasebeta

C2×#27136458 #37612944

order24736
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27136458

Splittings

SylowC773 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D773
commutatorC2×C773C22×C4
FrattiniC22C22×D773
FittingC22×C4×C773C2
socle, prime radicalC23×C773C22
cosocleC22×C773C23
hypercenterC22×C4D773
hypocenterC773C2×C4⋊C4
LCSG ▷ C2×C773 ▷ C773
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24736

Conjugacy classes & character table

6196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24736, 100);