Finite Group Databasebeta

C22×C22⋊#63214 #17186989

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊#63214

Splittings

SylowC17 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D17
commutatorC2×C17C23×C16
FrattiniC2×C8C23×D17
FittingC24×C8×C17C2
socleC24×C17C2×C8
prime radicalC25×C17C8
cosocleC2×C8×C17C24
hypercenterC24×C8D17
hypocenterC17C22×C22⋊C16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C8 ◁ C24×C8

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322233);