Finite Group Databasebeta

← Prev (#19099765) Next (#19099767) →

D17×(C5⋊D5)⋊C3 #19099766

order5100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productD17×(C5⋊D5)⋊C3
unambiguous semidirect product(D17×C5⋊D5)⋊C3

Splittings

Fitting, socle, derived, HallC52×C17 ⋊ C22×C3
HallD17×C5⋊D5 ⋊ C3
HallC17×C52⋊C3 ⋊ C22
HallC52⋊C3 ⋊ C2×D17
SylowC52 ⋊ C2×C3×D17
SylowC17 ⋊ C2×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C17C22×C3
LCSG ▷ C52×C17
UCSC1

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D17×(C5⋊D5)⋊C3, D17×C3⋊((C5⋊D5)⋊C3), D51×(C5⋊D5)⋊C3, …
maximal normal subgroup ofC3×D17×(C5⋊D5)⋊C3, C7×D17×(C5⋊D5)⋊C3
maximal quotient ofD17×(C5⋊D5)⋊C9, C3×D17×(C5⋊D5)⋊C3, D17×C3⋊((C5⋊D5)⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 69);