Finite Group Databasebeta

C2×#29507606 #44509875

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#29507606

Splittings

FittingC2×#95×C241 ⋊ C2
SylowC241 ⋊ C2×#388

Subgroups

subgroupG/H
centerC24C22×D241
commutatorC22×C241C23×C4
FrattiniC23C23×D241
FittingC2×#95×C241C2
socleC24×C241C23
prime radicalC24×D241C22
cosocleC23×C241C24
hypercenterC2×#95D241
hypocenterC241C2×#388
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C24 ◁ C2×#95

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

4856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 6940);