Finite Group Databasebeta

C2×#21418480 #28416860

order14912
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#21418480

Splittings

FittingC2×C16×C233 ⋊ C2
SylowC233 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22D1864
commutator, cosocleC8×C233C23
FrattiniC8C22×D233
FittingC2×C16×C233C2
socleC22×C233D8
prime radicalC2×D1864C2
hypercenterC2×C16D233
hypocenterC233C2×SD32
LCSG ▷ C8×C233 ▷ C4×C233 ▷ C2×C233 ▷ C233
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

3734 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 974);