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C3×C25×Dic41 #27134144

order12300
isoclinismisoclinic class of D41
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×Dic41

Splittings

derived, SylowC41 ⋊ C3×C4×C25
HallC3×C25×C41 ⋊ C4
HallC25×C41 ⋊ C3×C4
HallC3×C41 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D41
commutator, hypocenterC41C3×C4×C25
FrattiniC2×C5C3×C5×D41
FittingC2×C3×C25×C41C2
socle, prime radicalC2×C3×C5×C41C2×C5
cosocleC2×C5×C41C2×C3×C5
LCSG ▷ C41
UCSC1 ◁ C2×C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C25×Dic41, C32×C25×Dic41, C3×C25×Dic123
maximal normal subgroup ofC9×C25×Dic41, C32×C25×Dic41
maximal quotient ofC9×C25×Dic41, C32×C25×Dic41, C3×C25×Dic123

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 6);