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C11×C25×D61 #46776648

order33550
automorphism?
homologyAbelianization (H1) = C2×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×D61

Splittings

Fitting, HallC11×C25×C61 ⋊ C2
derived, SylowC61 ⋊ C2×C11×C25
HallC25×C61 ⋊ C2×C11
HallC11×C61 ⋊ C2×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25D61
commutator, hypocenterC61C2×C11×C25
FrattiniC5C5×C11×D61
FittingC11×C25×C61C2
socleC5×C11×C61C2×C5
prime radicalC5×C11×D61C5
cosocleC5×C61C2×C5×C11
LCSG ▷ C61
UCSC1 ◁ C11×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16775

Conjugacy classes & character table

8800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33550, 8);