Finite Group Databasebeta

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C4×#22627582 #49161125

order37504
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#22627582

Splittings

FittingC4×C4⋊C4×C293 ⋊ C2
SylowC293 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D293
commutatorC2×C293C22×C42
FrattiniC23C23×D293
FittingC4×C4⋊C4×C293C2
socle, cosocleC23×C293C24
prime radicalC23×D293C23
hypercenterC4×C4⋊C4D293
hypocenterC293C4×#117
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

5920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 6850);