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C22⋊C4×D1084 #46839187

order34688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×D1084

Splittings

FittingC4×C22⋊C4×C271 ⋊ C2
SylowC271 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D271
commutatorC22×C271C23×C4
FittingC4×C22⋊C4×C271C2
socle, cosocleC23×C271C24
prime radicalC23×D1084C2
hypercenterC4×C22⋊C4D271
hypocenterC271D4×C22⋊C4
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C23 ◁ C4×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8672

Conjugacy classes & character table

5450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 7333);