Finite Group Databasebeta

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C4⋊C4×C22⋊D293 #49161684

order37504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D293

Splittings

FittingC22×C4⋊C4×C293 ⋊ C2
SylowC293 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
FittingC22×C4⋊C4×C293C2
socle, cosocleC23×C293C24
prime radicalC22×C22⋊D293C22
hypercenterC22×C4⋊C4D293
hypocenterC293D4×C4⋊C4
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

5890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 7409);