Finite Group Databasebeta

C2×#29507547 #44509237

order30848
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#29507547

Splittings

SylowC241 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1928
commutatorC8×C241C22×C4
FrattiniC2×C8C22×D241
FittingC22×C16×C241C2
socleC22×C241#107
prime radicalC23×C241Q16
cosocleC2×C8×C241C23
hypercenterC22×C16D241
hypocenterC241C2×#368
LCSG ▷ C8×C241 ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

7724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 6302);