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D5×D23×C11⋊C5 #38760766

order25300
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD5×D23×C11⋊C5
unambiguous semidirect product(D5×C23)⋊(C2×C11⋊C5)
unambiguous semidirect product(C5×D23)⋊(C2×C11⋊C5)
unambiguous semidirect productD115⋊(C2×C11⋊C5)
unambiguous semidirect product(D5×C11×D23)⋊C5

Splittings

Fitting, socle, derivedC5×C11×C23 ⋊ C22×C5
HallC5×C23×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D23
HallC11×C23 ⋊ C2×C5×D5
SylowC23 ⋊ C2×D5×C11⋊C5
SylowC11 ⋊ C5×D5×D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C23C22×C5
LCSG ▷ C5×C11×C23
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1265

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 103);