Finite Group Databasebeta

C2×#27134365 #37589904

order24608
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27134365

Splittings

SylowC769 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D769
commutatorC2×C769C22×C4
FrattiniC4C22×D769
FittingC22×C4×C769C2
socleC22×C769C2×C4
prime radicalC23×C769C4
cosocleC4×C769C23
hypercenterC22×C4D769
hypocenterC769C2×M16
LCSG ▷ C2×C769 ▷ C769
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12304

Conjugacy classes & character table

6164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24608, 151);