Finite Group Databasebeta

C22×C4×#11745400 #28417495

order14912
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#11745400
unambiguous semidirect productD233⋊(C2×C42)

Splittings

FittingC22×C4×C233 ⋊ C4
derived, SylowC233 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#11745400
commutator, hypocenterC233C22×C42
FrattiniC2C23×#11745400
FittingC22×C4×C233C4
socleC23×C233C2×C4
prime radicalC23×D233C22
cosocleC2×D233C24
LCSG ▷ C233
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3728

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1609);