Finite Group Databasebeta

C4×C4⋊C4×D37 #17996929

order4736
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C4⋊C4×D37

Splittings

FittingC4×C4⋊C4×C37 ⋊ C2
SylowC37 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC2×C37C22×C42
FrattiniC23C23×D37
FittingC4×C4⋊C4×C37C2
socle, cosocleC23×C37C24
prime radicalC23×D37C23
hypercenterC4×C4⋊C4D37
hypocenterC37C2×C4×C4⋊C4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6843);