Finite Group Databasebeta

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Q82×C263 #30681628

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

Aliases

direct productQ82×C263

Subgroups

subgroupG/H
center, socle, prime radicalC22×C263C24
commutator, Frattini, cosocleC22C24×C263
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16832

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#46781825, #46781887, #46781968
maximal subgroup of#1623×C263, #1633×C263, #1645×C263, …
maximal normal subgroup of#1623×C263, #1633×C263, #1645×C263, …
maximal quotient ofQ8×C4⋊C4×C263, #2369×C263, #2451×C263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 239);