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C3×C41×Dic25 #27134145

order12300
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC3×C41×Dic25

Splittings

derived, SylowC25 ⋊ C3×C4×C41
HallC3×C25×C41 ⋊ C4
HallC25×C41 ⋊ C3×C4
HallC3×C25 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C41D25
commutator, hypocenterC25C3×C4×C41
FrattiniC2×C5C3×D5×C41
FittingC2×C3×C25×C41C2
socle, prime radicalC2×C3×C5×C41D5
cosocleC2×C25C2×C3×C41
LCSG ▷ C25
UCSC1 ◁ C2×C3×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C41×Dic25, C32×C41×Dic25, C3×C41×Dic75
maximal normal subgroup ofC9×C41×Dic25, C32×C41×Dic25
maximal quotient ofC9×C41×Dic25, C32×C41×Dic25, C3×C41×Dic75

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 7);