Finite Group Databasebeta

C2×#21418474 #28416849

order14912
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#21418474

Splittings

FittingC2×C16×C233 ⋊ C2
SylowC233 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D233
commutatorC2×C233C22×C8
FrattiniC8C22×D233
FittingC2×C16×C233C2
socleC22×C233C2×C8
prime radicalC22×D233C8
cosocleC8×C233C23
hypercenterC2×C16D233
hypocenterC233C2×M32
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

3752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44449949
maximal normal subgroup of#44449949

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 963);