Finite Group Databasebeta

C22×#16836602 #28417506

order14912
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16836602

Splittings

derived, SylowC233 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#11745400
commutator, hypocenterC233C23×C8
FrattiniC2C23×#11745400
FittingC22×C4×C233C4
socleC23×C233C2×C4
prime radicalC23×D233C4
cosocleDic233C24
LCSG ▷ C233
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

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, 1620);