Finite Group Databasebeta

C2×C22⋊#14272345 #28417402

order14912
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#14272345

Splittings

SylowC233 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#11745400
commutatorC2×C233C22×C8
FrattiniC22C22×#11745400
Fitting, prime radicalC24×C233C4
socleC23×C233C2×C4
cosocleC2×Dic233C23
hypercenterC24#11745400
hypocenterC233C2×C22⋊C8
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C23 ◁ C24

202 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, 1516);