Finite Group Databasebeta

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C4⋊C4×C22⋊D37 #17997495

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D37

Splittings

FittingC22×C4⋊C4×C37 ⋊ C2
SylowC37 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC22×C4⋊C4×C37C2
socle, cosocleC23×C37C24
prime radicalC22×C22⋊D37C22
hypercenterC22×C4⋊C4D37
hypocenterC37D4×C4⋊C4
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 7409);