Finite Group Databasebeta

C2×#29507574 #44509815

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#29507574

Splittings

FittingC22×C4⋊C4×C241 ⋊ C2
SylowC241 ⋊ C2×#380

Subgroups

subgroupG/H
centerC24C22×D241
commutatorC22×C241C23×C4
FrattiniC23C23×D241
FittingC22×C4⋊C4×C241C2
socleC24×C241C23
prime radicalC24×D241C22
cosocleC23×C241C24
hypercenterC22×C4⋊C4D241
hypocenterC241C2×#380
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C24 ◁ C22×C4⋊C4

1232 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, 6880);