Finite Group Databasebeta

D4×Q8×C283 #31826146

order18112
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C283 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C283

Subgroups

subgroupG/H
center, socleC22×C283C24
commutator, Frattini, cosocleC22C24×C283
prime radicalC2×D4×C283C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9056

Conjugacy classes & character table

7075 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49120364, #49120426, #49120510, …
maximal subgroup of#1627×C283, #1637×C283, #1649×C283, …
maximal normal subgroup of#1627×C283, #1637×C283, #1649×C283, …
maximal quotient ofQ8×C22⋊C4×C283, D4×C4⋊C4×C283, Q8×C4⋊C4×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 230);