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C22⋊C4×#63223 #17031958

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22⋊C4×#63223

Splittings

SylowC17 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D17
commutatorC22×C17C22×C42
FittingC2×C4×C22⋊C4×C17C2
socleC23×C17C23×C4
prime radicalC25×C17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C22⋊C4×M16
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167202);