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C4⋊C4×C22⋊D173 #36356462

order22144
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D173

Splittings

FittingC22×C4⋊C4×C173 ⋊ C2
SylowC173 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D173
commutatorC22×C173C23×C4
FittingC22×C4⋊C4×C173C2
socle, cosocleC23×C173C24
prime radicalC22×C22⋊D173C22
hypercenterC22×C4⋊C4D173
hypocenterC173D4×C4⋊C4
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11072

Conjugacy classes & character table

3490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 7409);