Finite Group Databasebeta

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C4×C31×C97⋊C3 #49115304

order36084
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C31×C97⋊C3
unambiguous semidirect product(C4×C97)⋊(C3×C31)

Splittings

Fitting, HallC4×C31×C97 ⋊ C3
derived, SylowC97 ⋊ C3×C4×C31
HallC31×C97 ⋊ C3×C4
HallC4×C97 ⋊ C3×C31

Subgroups

subgroupG/H
center, hypercenterC4×C31C97⋊C3
commutator, hypocenterC97C3×C4×C31
FrattiniC2C2×C31×C97⋊C3
FittingC4×C31×C97C3
socleC2×C31×C97C2×C3
prime radicalC2×C31×C97⋊C3C2
cosocleC2×C97C2×C3×C31
LCSG ▷ C97
UCSC1 ◁ C4×C31

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12028

Conjugacy classes & character table

4340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36084, 2);