Finite Group Databasebeta

C22×#16836584 #28417211

order14912
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16836584

Splittings

SylowC233 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D233
commutator, cosocleC4×C233C24
FrattiniC4C23×D233
FittingC22×Q8×C233C2
socle, prime radicalC23×C233D4
hypercenterC22×Q8D233
hypocenterC233C22×Q16
LCSG ▷ C4×C233 ▷ C2×C233 ▷ C233
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14912

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1325);