Finite Group Databasebeta

C2×#27160964 #38745137

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#27160964

Splittings

SylowC197 ⋊ C2×#387

Subgroups

subgroupG/H
centerC24C22×D197
commutatorC22×C197C23×C4
FrattiniC23C23×D197
FittingC2×#95×C197C2
socle, prime radicalC24×C197C23
cosocleC23×C197C24
hypercenterC2×#95D197
hypocenterC197C2×#387
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C24 ◁ C2×#95

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Conjugacy classes & character table

3976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 6935);