Finite Group Databasebeta

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D4×Q8×C199 #27163699

order12736
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C199 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C199

Subgroups

subgroupG/H
center, socleC22×C199C24
commutator, Frattini, cosocleC22C24×C199
prime radicalC2×D4×C199C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C199 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6368

Conjugacy classes & character table

4975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38767953, #38768015, #38768099, …
maximal subgroup of#1627×C199, #1637×C199, #1649×C199, …
maximal normal subgroup of#1627×C199, #1637×C199, #1649×C199, …
maximal quotient ofQ8×C22⋊C4×C199, D4×C4⋊C4×C199, Q8×C4⋊C4×C199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12736, 230);