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C2×D21×C11⋊C25 #37528258

order23100
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D21×C11⋊C25
unambiguous semidirect product(C2×C3)⋊(D7×C11⋊C25)
unambiguous semidirect product(C2×C7)⋊(D3×C11⋊C25)
unambiguous semidirect product(C2×C11×D21)⋊C25

Splittings

derived, HallC3×C7×C11 ⋊ C22×C25
HallC3×C7×C11⋊C25 ⋊ C22
HallC7×C11⋊C25 ⋊ C2×D3
HallC2×C11×D21 ⋊ C25
HallC3×C11⋊C25 ⋊ C2×D7
HallC7×C11 ⋊ C2×D3×C25
HallC3×C11 ⋊ C2×D7×C25
HallC3×C7 ⋊ C22×C11⋊C25
SylowC11 ⋊ C2×C25×D21
SylowC7 ⋊ C2×D3×C11⋊C25
SylowC3 ⋊ C2×D7×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5D21×C11⋊C5
commutator, hypocenterC3×C7×C11C22×C25
FrattiniC5C2×D21×C11⋊C5
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C5×C11×D21C5
cosocleC3×C5×C7×C11C22×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 69);