Finite Group Databasebeta

C22×#11762638 #17187375

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11762638

Splittings

SylowC17 ⋊ C22×#368

Subgroups

subgroupG/H
centerC22×C4#63228
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC22×C17×#108C2
socleC23×C17#107
prime radicalC24×C17Q16
cosocleC2×C8×C17C24
hypercenterC22×#108D17
hypocenterC17C22×#368
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322619);