Finite Group Databasebeta

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C4×C61×C52⋊C3 #32912975

order18300
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C5

Aliases

direct productC4×C61×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C3×C61)

Splittings

Fitting, HallC4×C52×C61 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C61
HallC52×C61 ⋊ C3×C4
HallC4×C52 ⋊ C3×C61

Subgroups

subgroupG/H
center, hypercenterC4×C61C52⋊C3
commutator, hypocenterC52C3×C4×C61
FrattiniC2C2×C61×C52⋊C3
FittingC4×C52×C61C3
socleC2×C52×C61C2×C3
prime radicalC2×C61×C52⋊C3C2
cosocleC2×C52C2×C3×C61
LCSG ▷ C52
UCSC1 ◁ C4×C61

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3660

Conjugacy classes & character table

2684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 98);