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C3×C5×Dic3×C107 #34064102

order19260
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C107 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C107
unambiguous semidirect productC3⋊(C3×C4×C5×C107)

Splittings

derivedC3 ⋊ C3×C4×C5×C107
HallC32×C5×C107 ⋊ C4
HallC32×C107 ⋊ C4×C5
HallC32×C5 ⋊ C4×C107
SylowC32 ⋊ C4×C5×C107

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C107D3
commutator, hypocenterC3C3×C4×C5×C107
FrattiniC2C3×C5×D3×C107
Fitting, socle, prime radicalC2×C32×C5×C107C2
cosocleC2×C3C2×C3×C5×C107
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C107

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6420

Conjugacy classes & character table

9630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19260, 33);