Finite Group Databasebeta

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C4×C31⋊C3×C97 #49115305

order36084
automorphism?
homologyAbelianization (H1) = C3×C4×C97 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC4×C31×C97 ⋊ C3
derived, SylowC31 ⋊ C3×C4×C97
HallC31×C97 ⋊ C3×C4
HallC4×C31 ⋊ C3×C97

Subgroups

subgroupG/H
center, hypercenterC4×C97C31⋊C3
commutator, hypocenterC31C3×C4×C97
FrattiniC2C2×C31⋊C3×C97
FittingC4×C31×C97C3
socleC2×C31×C97C2×C3
prime radicalC2×C31⋊C3×C97C2
cosocleC2×C31C2×C3×C97
LCSG ▷ C31
UCSC1 ◁ C4×C97

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12028

Conjugacy classes & character table

5044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36084, 3);