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C3×C25×Dic109 #45658167

order32700
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×Dic109

Splittings

derived, SylowC109 ⋊ C3×C4×C25
HallC3×C25×C109 ⋊ C4
HallC25×C109 ⋊ C3×C4
HallC3×C109 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D109
commutator, hypocenterC109C3×C4×C25
FrattiniC2×C5C3×C5×D109
FittingC2×C3×C25×C109C2
socle, prime radicalC2×C3×C5×C109C2×C5
cosocleC2×C5×C109C2×C3×C5
LCSG ▷ C109
UCSC1 ◁ C2×C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32700

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 3);