Finite Group Databasebeta

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C4⋊C4×Dic346 #36356478

order22144
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic346

Splittings

SylowC173 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D173
commutatorC22×C173C23×C4
FittingC4×C4⋊C4×C173C2
socle, prime radical, cosocleC23×C173C24
hypercenterC4×C4⋊C4D173
hypocenterC173Q8×C4⋊C4
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C23 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22144

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, 7425);