Finite Group Databasebeta

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C4×C52⋊C3×C109 #45658232

order32700
automorphism?
homologyAbelianization (H1) = C3×C4×C109 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊C3×C109
unambiguous semidirect product(C4×C52)⋊(C3×C109)

Splittings

Fitting, HallC4×C52×C109 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C109
HallC52×C109 ⋊ C3×C4
HallC4×C52 ⋊ C3×C109

Subgroups

subgroupG/H
center, hypercenterC4×C109C52⋊C3
commutator, hypocenterC52C3×C4×C109
FrattiniC2C2×C52⋊C3×C109
FittingC4×C52×C109C3
socleC2×C52×C109C2×C3
prime radicalC2×C52⋊C3×C109C2
cosocleC2×C52C2×C3×C109
LCSG ▷ C52
UCSC1 ◁ C4×C109

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

4796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 68);