Finite Group Databasebeta

← Prev (#44545636) Next (#44545638) →

C4×C52⋊C3×C107 #44545637

order32100
automorphism?
homologyAbelianization (H1) = C3×C4×C107 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊C3×C107
unambiguous semidirect product(C4×C52)⋊(C3×C107)
unambiguous semidirect product(C4×C52×C107)⋊C3

Splittings

Fitting, HallC4×C52×C107 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C107
HallC52×C107 ⋊ C3×C4
HallC4×C52 ⋊ C3×C107

Subgroups

subgroupG/H
center, hypercenterC4×C107C52⋊C3
commutator, hypocenterC52C3×C4×C107
FrattiniC2C2×C52⋊C3×C107
FittingC4×C52×C107C3
socleC2×C52×C107C2×C3
prime radicalC2×C52⋊C3×C107C2
cosocleC2×C52C2×C3×C107
LCSG ▷ C52
UCSC1 ◁ C4×C107

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6420

Conjugacy classes & character table

4708 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 35);