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C107×C22⋊(C52⋊C3) #44545703

order32100
automorphism?
homologyAbelianization (H1) = C3×C107 · Schur multiplier (H2) = C2×C5

Aliases

direct productC107×C22⋊(C52⋊C3)
unambiguous semidirect productC22⋊(C52⋊C3×C107)
unambiguous semidirect productC52⋊(A4×C107)
unambiguous semidirect product(C22×C107)⋊(C52⋊C3)
unambiguous semidirect product(C52×C107)⋊A4

Splittings

Fitting, socle, HallC22×C52×C107 ⋊ C3
derived, HallC22×C52 ⋊ C3×C107
HallC52×C107 ⋊ A4
HallC22×C107 ⋊ C52⋊C3
SylowC52 ⋊ A4×C107
SylowC22 ⋊ C52⋊C3×C107

Subgroups

subgroupG/H
center, hypercenterC107C22⋊(C52⋊C3)
commutator, cosocle, hypocenterC22×C52C3×C107
FrattiniC1G
Fitting, socleC22×C52×C107C3
LCSG ▷ C22×C52
UCSC1 ◁ C107

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3210

Conjugacy classes & character table

3852 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 101);