Finite Group Databasebeta

C22×#11761618 #16864172

order4288
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11761618

Splittings

SylowC67 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D67
commutator, cosocleC4×C67C24
FrattiniC4C23×D67
FittingC22×Q8×C67C2
socle, prime radicalC23×C67D4
hypercenterC22×Q8D67
hypocenterC67C22×Q16
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 1325);