Finite Group Databasebeta

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D4×Q8×C263 #30681619

order16832
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C263 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C263

Subgroups

subgroupG/H
center, socleC22×C263C24
commutator, Frattini, cosocleC22C24×C263
prime radicalC2×D4×C263C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#46781850, #46781912, #46781996, …
maximal subgroup of#1627×C263, #1637×C263, #1649×C263, …
maximal normal subgroup of#1627×C263, #1637×C263, #1649×C263, …
maximal quotient ofQ8×C22⋊C4×C263, D4×C4⋊C4×C263, Q8×C4⋊C4×C263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 230);