Finite Group Databasebeta

C4×C53×#3862 #44528369

order31164
automorphism?
homologyAbelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C7

Aliases

direct productC4×C53×#3862

Splittings

Fitting, HallC4×C72×C53 ⋊ C3
derived, SylowC72 ⋊ C3×C4×C53
HallC72×C53 ⋊ C3×C4
HallC4×C72 ⋊ C3×C53

Subgroups

subgroupG/H
center, hypercenterC4×C53#3862
commutator, hypocenterC72C3×C4×C53
FrattiniC2C2×C53×#3862
FittingC4×C72×C53C3
socleC2×C72×C53C2×C3
prime radicalC2×C53×#3862C2
cosocleC2×C72C2×C3×C53
LCSG ▷ C72
UCSC1 ◁ C4×C53

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4452

Conjugacy classes & character table

4028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 61);