Finite Group Databasebeta

← Prev (#30681614) Next (#30681616) →

D42×C263 #30681615

order16832
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C263 · Schur multiplier (H2) = C26

Aliases

direct productD42×C263

Subgroups

subgroupG/H
center, socleC22×C263C24
commutator, Frattini, cosocleC22C24×C263
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4208

Conjugacy classes & character table

6575 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46781801, #46781863, #46781926
maximal subgroup of#1619×C263, #1629×C263, #1639×C263, …
maximal normal subgroup of#1619×C263, #1629×C263, #1639×C263, …
maximal quotient ofD4×C22⋊C4×C263, D4×C4⋊C4×C263, #2358×C263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 226);