Finite Group Databasebeta

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C2×C4⋊C4×Dic37 #17996933

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

Aliases

direct productC2×C4⋊C4×Dic37

Splittings

SylowC37 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D37
commutatorC2×C37C22×C42
FrattiniC23C23×D37
FittingC22×C4⋊C4×C37C2
socle, prime radicalC24×C37C23
cosocleC23×C37C24
hypercenterC22×C4⋊C4D37
hypocenterC37C2×C4×C4⋊C4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

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, 6847);