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C4×#22551570 #45666853

order32896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#22551570

Splittings

FittingC4×C4⋊C4×C257 ⋊ C2
SylowC257 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D257
commutatorC22×C257C23×C4
FrattiniC23C23×D257
FittingC4×C4⋊C4×C257C2
socle, cosocleC23×C257C24
prime radicalC23×D257C23
hypercenterC4×C4⋊C4D257
hypocenterC257C4×C22⋊Q8
LCSG ▷ C22×C257 ▷ C257
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16448

Conjugacy classes & character table

5176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 7043);