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C3×C73×Dic25 #36346376

order21900
automorphism?
homologyAbelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1

Aliases

direct productC3×C73×Dic25

Splittings

derived, SylowC25 ⋊ C3×C4×C73
HallC3×C25×C73 ⋊ C4
HallC25×C73 ⋊ C3×C4
HallC3×C25 ⋊ C4×C73

Subgroups

subgroupG/H
center, hypercenterC2×C3×C73D25
commutator, hypocenterC25C3×C4×C73
FrattiniC2×C5C3×D5×C73
FittingC2×C3×C25×C73C2
socle, prime radicalC2×C3×C5×C73D5
cosocleC2×C25C2×C3×C73
LCSG ▷ C25
UCSC1 ◁ C2×C3×C73

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21900

Conjugacy classes & character table

6132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21900, 4);