Finite Group Databasebeta

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C4×C11⋊C5×C97 #36319341

order21340
automorphism?
homologyAbelianization (H1) = C4×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11⋊C5×C97
unambiguous semidirect product(C4×C11)⋊(C5×C97)
unambiguous semidirect product(C4×C11×C97)⋊C5

Splittings

Fitting, HallC4×C11×C97 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C97
HallC11×C97 ⋊ C4×C5
HallC4×C11 ⋊ C5×C97

Subgroups

subgroupG/H
center, hypercenterC4×C97C11⋊C5
commutator, hypocenterC11C4×C5×C97
FrattiniC2C2×C11⋊C5×C97
FittingC4×C11×C97C5
socleC2×C11×C97C2×C5
prime radicalC2×C11⋊C5×C97C2
cosocleC2×C11C2×C5×C97
LCSG ▷ C11
UCSC1 ◁ C4×C97

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4268

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21340, 2);