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C5×Dic15×C109 #45658237

order32700
automorphism?
homologyAbelianization (H1) = C4×C5×C109 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic15×C109
unambiguous semidirect productC3⋊(C5×Dic5×C109)

Splittings

derivedC3×C5 ⋊ C4×C5×C109
HallC3×C52×C109 ⋊ C4
HallC52×C109 ⋊ Dic3
HallC3×C109 ⋊ C5×Dic5
HallC3×C52 ⋊ C4×C109
SylowC52 ⋊ Dic3×C109
SylowC3 ⋊ C5×Dic5×C109

Subgroups

subgroupG/H
center, hypercenterC2×C5×C109D15
commutator, hypocenterC3×C5C4×C5×C109
FrattiniC2C5×D15×C109
Fitting, socle, prime radicalC2×C3×C52×C109C2
cosocleC2×C3×C5C2×C5×C109
LCSG ▷ C3×C5
UCSC1 ◁ C2×C5×C109

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

9810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 73);