Finite Group Databasebeta

← Prev (#23756260) Next (#23756262) →

D21⋊D119 #23756261

order9996
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD21⋊D119

Splittings

Fitting, socle, derived, HallC3×C72×C17 ⋊ C22
HallC72×C17 ⋊ C2×D3
HallC3×C72 ⋊ C2×D17
HallC3×C17 ⋊ D72
SylowC72 ⋊ D3×D17
SylowC17 ⋊ D21⋊D7
SylowC3 ⋊ D7×D119

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C17C22
LCSG ▷ C3×C72×C17
UCSC1

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,7^2,17|d^a=d^6,e^a=e^6,f^a=f^16,c^b=c^2,d^b=d^6

Conjugacy classes & character table

723 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11725071⋊D17, D63⋊D119, #44472784, …
maximal normal subgroup of#44472809, (C3⋊AGL(1,𝔽7))⋊D119, #44472837, …
maximal quotient ofD63⋊D119, C3×D21⋊D119, D21⋊D357, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 164);