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C3×C61×Dic25 #32912890

order18300
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productC3×C61×Dic25

Splittings

derived, SylowC25 ⋊ C3×C4×C61
HallC3×C25×C61 ⋊ C4
HallC25×C61 ⋊ C3×C4
HallC3×C25 ⋊ C4×C61

Subgroups

subgroupG/H
center, hypercenterC2×C3×C61D25
commutator, hypocenterC25C3×C4×C61
FrattiniC2×C5C3×D5×C61
FittingC2×C3×C25×C61C2
socle, prime radicalC2×C3×C5×C61D5
cosocleC2×C25C2×C3×C61
LCSG ▷ C25
UCSC1 ◁ C2×C3×C61

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18300

Conjugacy classes & character table

5124 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 13);