Finite Group Databasebeta

C2×#21418610 #28417492

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

Aliases

direct productC2×#21418610

Splittings

SylowC233 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#11745400
commutatorC2×C233C22×C8
FrattiniC4C22×#11745400
FittingC2×C8×C233C4
socleC22×C233C2×C8
prime radicalC22×D233C8
cosocle#14272338C23
hypercenterC2×C8#11745400
hypocenterC233C2×M32
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C2×C4 ◁ C2×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1606);