Finite Group Databasebeta

C2×C22⋊#15691005 #38734060

order24896
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#15691005

Splittings

SylowC389 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D389
commutatorC2×C389C22×C8
FrattiniC2×C4C22×D389
FittingC23×C4×C389C2
socleC23×C389C2×C4
prime radicalC24×C389C4
cosocleC2×C4×C389C23
hypercenterC23×C4D389
hypocenterC389C2×C22⋊C8
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

6248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 510);