Finite Group Databasebeta

C2×#29507478 #44507152

order30848
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#29507478

Splittings

SylowC241 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4C22⋊D241
commutatorC4×C241C2×C42
FrattiniC22×C4C22×D241
FittingC22×M16×C241C2
socleC23×C241C22⋊C4
prime radicalC24×C241D4
cosocleC22×C4×C241C23
hypercenterC22×M16D241
hypocenterC241C2×#339
LCSG ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7712

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, 4217);